The Heritage Foundation has approached one of the Senate’s leading anti-Trump Republicans, Ben Sasse, to gauge his interest in serving as president — an indication the influential conservative think tank mayturn away from its supportive posture toward the president.

Sasse, who was elected to his first term in the Senate in 2014, has swatted down the overtures from Heritage’s board of trustees, according to two sources familiar with the recruitment effort. The Nebraska senator rose to national prominence when he announced early in the primary calendar that he would support neither Donald Trump nor Hillary Clinton, and he has been a persistent critic of Trump ever since.

The entreaties are one sign that Heritage may be looking to change course after the May ouster of its former president, Jim DeMint. In the Senate, DeMint was a leading antagonist of establishment Republicans, and at Heritage he suffered from the perception that the organization was becoming too political — and too reflexively pro-Trump — as its focus on scholarship fell by the wayside.

The Ivy League-educated, 45-year-old Sasse was a college president before he was elected to the Senate, and he approached his job in Washington with an academic bearing. His vocal criticism of Trump, which homed in on what he considered the candidate’s insufficient appreciation for constitutional checks and balances, angered many Republicans.

“My current answer for who I would support in a hypothetical matchup between Mr. Trump and Mrs. Clinton is: Neither of them,” Sasse wrote in a Facebook post addressed to Trump supporters in February 2016. “I sincerely hope we select one of the other GOP candidates, but if Donald Trump ends up as the GOP nominee, conservatives will need to find a third option.”

A Trump alternative, of course, failed to emerge, and Sasse’s criticism of the man who is now president has continued into the administration. While Trump has continually promised to bring back factory jobs that disappeared due to globalization, Sasse has argued that it’s “crazy to mislead people and say we’re going to bring back all of the big factory jobs by creating a protectionist regime.”

He called the president’s intention to launch a cybersecurity initiative with Russian President Vladimir Putin “inexplicably bizarre.”

Some anti-Trump conservatives, including Weekly Standard editor-at-large Bill Kristol, looked to Sasse himself as a third option for president, urging him to run as a third-party candidate.

“I think Ben Sasse should be president of the United States, not president of Heritage, probably, but other than that it’s a good thing,” Kristol said of the organization’s appeals to the Nebraska senator.

But a spokesman for Sasse, James Wegmann, said the senator has no plans to leave the Senate. “If you ask me if he’ll consider an offer to be the Huskers’ offensive coordinator, I’ll dodge. But the answer to these Heritage rumors is simple: Nope.”

Kay Coles James, a member of the Heritage Foundation Board of Trustees’ Presidential Search Committee, said in a statement that the group is considering more than 200 people for the job, “many of them nationally renowned. We have engaged a professional search firm and we look forward to reviewing the candidates they suggest.”

The organization’s interest in Sasse — sources say board members have been persistent to the point of irritating the senator — indicates that it is looking for a reset. Other conservative think tanks have been less explicitly pro-Trump than Heritage was under DeMint. While American Enterprise Institute President Arthur Brooks, for example, has sought to explain the source of Trump’s support, he has stopped short of expressing support for him.

DeMint’s departure came on the heels of bitter disputes within the organization, with some charging that interim Heritage President Edwin Feulner’s protégé, Mike Needham, the head of Heritage Action, the group’s lobbying arm,had engineered his removal with an eye to taking control of the organization. Others argued that DeMint had proved a disappointing leader who had ceded the organization’s role as the brain trust of the GOP.

If Sasse won’t be the think tank’s next president, he represents a model of what its board of trustees — which last month hired the search firm to assist in its recruitment — may be on the lookout for.

Before he was elected to the Senate, Sasse worked as a consultant focused on revitalizing failing businesses — he has called himself a “crisis turnaround guy” — and then as a college president. Midland University in Nebraska, which he led for five years before he stepped down to run for office, was virtually bankrupt when he took over in 2009 and went on to become the fastest growing university in the region under his stewardship.

Though the GOP holds more power than it has in a decade, many argue that it needs an ideological revitalization. The Heritage Foundation played that role in the late 1970s, when it drew up thousands of detailed policies, known as the “Mandate for Leadership,” that came to serve as the policy engine of the Reagan administration.

Even if Sasse won’t be doing that from the helm of the Heritage Foundation, he’s made clear he has an interest in doing so from the Senate. In his maiden floor speech in 2015, he reminded his colleagues that the purpose of the institution was “to shield lawmakers from obsession with short-term popularity to enable us to focus on the biggest long-term challenges our people face.”